Dice Rolling variant [Archive] - Wizards Community

Post/Author/DateTimePost
imperialjunkie

05-11-05, 12:49 PM
I had a question about a dice rolling variant in Unearthed Arcana. I'm thinking of using the Defense Roll for the players in my campaign, which means that instead of the NPC/creatures making attack rolls, the PC's make the defense roll. This is based on creating an Attack Score for the creature/NPC. That score in Unearthed Arcana is based on: 11 + enemy's attack bonus. This in effect creates something similar to a static AC that the players roll against to see if they defend against their enemy's attack.

My question is this: Why is this Attack Score based off of an 11 instead of a 10? If AC is based off of a 10 with bonuses added, then why is this changed for an Attack Score?

Sorry if this is esoteric, but I'd like to use this variant to allow for players to roll more and me to roll less.

Thanks for anyone who has info/opinion.
tarkin

05-11-05, 01:07 PM
Attack Score is based on 11 because you have to BEAT the Defense roll.
imperialjunkie

05-12-05, 01:03 AM
Attack Score is based on 11 because you have to BEAT the Defense roll.
Something didn't seem right, which is why I posted this question in the first place. Your answer motivated me to work out the math. I just ran the numbers on this variant (Players Roll All The Dice- pg. 133 of Unearthed Arcana), and I think it is an error. I originally thought the variant gave NPC's the edge, but actually the PC will always have a 5% advantage. They apparently figured this variant as if a d20 was 0-20 instead of 1-20.

This was easiest to test by comparing two evenly matched combatants. For instance, two individuals are fighting who each have a +2 attack bonus and defense modifiers of +6. The PC's enemy then has an AC of 16 and an Attack Score of 13 (11 + attack bonus of 2). With this variant, only the player rolls- the DM does no rolling. In this case, the player must roll a 14 or higher to hit the NPC (roll of 14 + attack bonus of 2 = AC of 16). This means the PC has a 35% chance of hitting the NPC. Conversely, the player must roll a 7 or higher to avoid being hit by the NPC (roll of 7 + defense modifier of +6 = Attack Score of 13). This means the PC has a 70% chance of avoiding the NPC's attack.

In other words, these two evenly matched combatants are not evenly matched by this dice variant. The PC has a 35% chance of hitting, while the NPC only has a 30% chance of hitting. This 5% discrepancy works out no matter what numbers you put in.

The numbers for this variant in Unearthed Arcana should be as follows:

Attack Score: 12 + enemy's attack bonus

or...

Change the wording so that the player's defense roll must exceed the Attack Score of the NPC. As it reads now, the player must equal or exceed the Attack Score.

This probably works out the same for Saving Throws and Save Scores and Spell Resistance on pg. 133-134.

I know this seems nitpicky, but I think this is a great variant as it gets the players rolling more without bogging play down. Only players roll in combat- DM does not. But to make it work, the numbers need to be changed.
shift244

05-12-05, 04:22 AM
You might be making things more complicated than it actually is.. or I'm just simple, but Tarkin has posted it as I see it, if not perhaps clear enough to you.

The matter is a simple equation of Attack+1d20 >= AC+1d20 equals HIT.

The normal assumption, by using a base AC of 10 instead of a 1d20 roll splits the possibility in to 50%, by giving us Attack+1d20 >= AC+10.


Now we reverse the equation from the MISS point of view.

We have Attack+1d20 < AC+120 equals MISS.
Simplifying dice rolls we get: Attack+10 < AC+1d20. or Attack+11 <= AC+1d20.

At least, that is how I understand the situation. ;)
imperialjunkie

05-12-05, 12:06 PM
Both you and Tarkin lay out the concept well that a hit must be equal to or greater than the AC, and thus basing the static Attack Score on an 11 rather than a 10 makes sense. Got that.

What I don't understand-- and I am no mathematician-- is how this concept then works out to a 5% discrepency. It would seem that basing the Attack Score on an 11 instead of a 10 would even the odds between 2 equal combatants. But in actuality it doesn't even them enough when you run the numbers.

Again, I'm not misunderstanding the concept. I'm just not understanding why the concept doesn't work out into equal probability of hits and misses between equal combatants.

Here's the formula for this variant (again- based on pg. 133 of Unearthed Arcana):

1d20 + PC attack bonus >= NPC Armor Class = hit landed by PC
1d20 + PC defense modifier >= NPC Attack Score [11 + attack bonus] = hit avoided by PC

Plug in any random numbers for attack bonus and defense modifier ...

PC attack bonus +7/ PC defense modifier +3
NPC attack bonus +7/ NPC defense modifier +3

Run the formula with x being the result on a 1d20...

x + 7 >= 13 = successful hit
x >= 6 = successful hit
An attack roll of 6 or higher on a d20 is a successful hit by the PC.
This is a 75% chance of a hit by the PC, or a 25% chance of missing.

x + 3 >= 18 = successful defense
x >= 15 = successful defense
A defense roll of 15 or higher is a successful defense by the PC.
This is a 30% chance of a miss by the NPC, or a 70% chance of hitting.

Again, a 5% discrepancy. Always works out that way.

It looks to me like the correct defense roll formula should then be:
1d20 + defense modifiers > NPC Attack Score = hit avoided by PC

Or to be more specific, in paragraph 1 under Attacking and Defending under Players Roll All The Dice on pg. 133 of Unearthed Arcana it seems like it should read:

If that defense check exceeds the attack score of the enemy, the attack misses.

It currently reads "equals or exceeds."

Yes I'm overdoing it, and yes I'm a nerd, but I want to use this variant. :D
Can anyone show me how I might be misunderstanding the math? I am open to correction, and I understand what tarkin and shift are saying. I just want to see it worked out.
imperialjunkie

05-12-05, 03:25 PM
After further thought, I think I'm just going to use a straight-up Attack Roll/Defense Roll variant from the DM Guide. This Unearthed Arcana variant is too complicated.

Thanks for the thoughts from tarkin and shift244
Inigo Carmine

05-12-05, 04:36 PM
Junkie, there is no 5% discrepancy; you are looking at the defensive roll incorrectly.

under normal rules of rolling an attack vs a defense, if the attack meets or exceeds the defense, the attack is successful. If the defense exceeds the attack, the attack is not successful. (Note that if the defense meets the attack, the attack succeeds).

you're making a mistake in assuming that with the defense roll variant, if the PC's defense roll meets the attac roll, the attack was unsuccessful. This is wrong. The PC's defense roll *MUST BEAT* the attack roll.


in your example here:
This was easiest to test by comparing two evenly matched combatants. For instance, two individuals are fighting who each have a +2 attack bonus and defense modifiers of +6. The PC's enemy then has an AC of 16 and an Attack Score of 13 (11 + attack bonus of 2). With this variant, only the player rolls- the DM does no rolling. In this case, the player must roll a 14 or higher to hit the NPC (roll of 14 + attack bonus of 2 = AC of 16). This means the PC has a 35% chance of hitting the NPC. Conversely, the player must roll a 7 or higher to avoid being hit by the NPC (roll of 7 + defense modifier of +6 = Attack Score of 13). This means the PC has a 70% chance of avoiding the NPC's attack.

The bold part is your mistake. If the PC rolls a 7, the defense roll equals the attack roll (both = 14), and the attack succeeds. The PC must roll an 8 or higher on his defense roll, meaning he has a 65% chance to be hit. Therefore things are completely even.

In creating the active defense rolls, there were two concepts that opposed eachother, and they could only keep one:

1) In an attack vs armor situation, an attack succeeds if it meets or beats the armor class. This is the one they kept.

2) When you roll against a fixed number, the person rolling wins the tie. This is what they removed in this variant rule, but you mistakenly kept.



==============
I don't own unearthed arcana, but I will say this: this still gives the PCs a strong advantage because the enemy can't get a critical hit in (Unless there are other rules for for it regaurding the PC rolling 1, 2, 3 (for 20, 19-20, 18-20 threat ranged) on his defense roll).
imperialjunkie

05-16-05, 01:48 PM
I didn't look at this a few days ago because I scrapped the idea of using this variant. I just took a peek and so I'll respond.

I completely agree with you Inigo, and I am not wrong at the same time. What you are describing is the mistake that Unearthed Arcana makes on this variant. On pg. 133, it says, "If that defense check equals or exceeds the attack score of the enemy, the attack misses." It needs to be corrected to "If that defense check exceeds the attack score of the enemy, the attack misses." This evens out the odds. The principle you are describing in your post was overlooked by the developer of this variant. Probably should be errata, but it's probably not important enough to put something out. I don't think they have any errata for Unearthed Arcana.

The bottom line for me, which is the bottom line on most variants, is that you have to work out so many other issues that it becomes too tedious to use. As I said above, I'm going to use the common Attack Roll vs. Defense Roll variant in the DMG. This adds some randomness to defense instead of just 'taking 10' as AC usually assumes for defense.

Junkie, there is no 5% discrepancy; you are looking at the defensive roll incorrectly.

under normal rules of rolling an attack vs a defense, if the attack meets or exceeds the defense, the attack is successful. If the defense exceeds the attack, the attack is not successful. (Note that if the defense meets the attack, the attack succeeds).

you're making a mistake in assuming that with the defense roll variant, if the PC's defense roll meets the attac roll, the attack was unsuccessful. This is wrong. The PC's defense roll *MUST BEAT* the attack roll.


in your example here:


The bold part is your mistake. If the PC rolls a 7, the defense roll equals the attack roll (both = 14), and the attack succeeds. The PC must roll an 8 or higher on his defense roll, meaning he has a 65% chance to be hit. Therefore things are completely even.

In creating the active defense rolls, there were two concepts that opposed eachother, and they could only keep one:

1) In an attack vs armor situation, an attack succeeds if it meets or beats the armor class. This is the one they kept.

2) When you roll against a fixed number, the person rolling wins the tie. This is what they removed in this variant rule, but you mistakenly kept.



==============
I don't own unearthed arcana, but I will say this: this still gives the PCs a strong advantage because the enemy can't get a critical hit in (Unless there are other rules for for it regaurding the PC rolling 1, 2, 3 (for 20, 19-20, 18-20 threat ranged) on his defense roll).
mercurial67

05-16-05, 09:13 PM
imperialjunkie is correct in his assesment of the error made. It is very difficult to describe the problem (unless you are a mathemetician, which I am not).

To make everything simple, I'll use an example of someone with an AC of 10 being attacked by someone with +0 to hit.

It boils down to this - They hit by rolling 10 on a d20. That gives them 11/20 chances of hitting (10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 - this will be important later on). That also gives them 9/20 chances of missing. So if we want the person being attacked to roll and we use the higher is better, they would be missed by rolling 12, 13, 14, 15, 16, 17, 18, 19, 20 (count them, it's 9 chances).

The problem lies in it is not a 50/50 chance of hitting/missing. There is a difference of 2 between them, not 1. You have to figure out the odds of missing instead of the odds of hitting. The correct method is to change it so the attack score is 12+attack bonus.
Inigo Carmine

05-16-05, 09:16 PM
haha. So Wizards made the mistake and not the junkie. I appologize for assuming it was you. As I think I said, I don't actually have UA.

-Inigo
Nom

05-16-05, 11:20 PM
Note that the defense roll variant as presented in the DMG is somewhat broken. Rolling once per round for AC creates all sorts of bizarre mechanics on high or low rolls. On a high roll, everyone attacks a different target for the round or performs other activities because "we can't hit him anyway". On a low roll, everyone gangs up and exploits the vulnerable target.

To compare, consider the effect of allowing an attacker to use a single attack roll for all attacks. It can break badly for exceptional rolls (especially a 20).

If you are going to use defense rolls, you really need to roll a new defense roll every time the AC is tested.

Note 1: Using a defense roll slightly penalises the attacker in most situations. When the attacker's modifier is 5 less than the defender's then the probability of a hit is the same as if the defender takes 10. If the attacker's advantage is greater than -5 (ie -5, -4, ..., 0, or positive) then the attacker is slightly worse off.

Note 2: More generally, any mechanic where a single roll is opposed to many checks is bad, as it tends to result in "all or nothing" effects. AC and DCs get this right. Turning undead gets this wrong, which is why I use a variant where undead receive a Will save against a fixed DC from the cleric rather than a simple "modified check result vs HD" comparison.
imperialjunkie

05-17-05, 12:36 AM
I like your thoughts Nom. I especially like the idea about the Will save for undead. I"ll consider that.

If I were to do the defense roll variant from the DMG, I'd do an opposed roll against every attack by the PCs and allow them to do the same. One main reason would be to get them rolling more dice. But I'd also like some more randomness to defense.
Nom

05-17-05, 01:41 AM
I like your thoughts Nom. I especially like the idea about the Will save for undead. I"ll consider that.My current house rules on the topic are at http://users.bigpond.net.au/nom/d20/games/rules/combat.html#turn_undead. Note that I haven't stress tested them yet, and am happy to hear feedback.

Under this rule, turn undead uses basically the same mechanic as sleep, rather than its own bizarre mechanic. If you like opposed rolls, you may wish to use an opposed roll for the DC.
shift244

05-17-05, 08:31 PM
haha. So Wizards made the mistake and not the junkie. I appologize for assuming it was you. As I think I said, I don't actually have UA.

-InigoIs it? While PCs might be generally tougher than the oppositions they combat, they are also generally outnumbered, in the long run. The slight bias might be an intentional probability weight to increase the PCs survivalbility. :D